The helix and the helicoid

A helix is a curve in three dimensions - in other words, a space curve - the tangent to which makes a constant angle with a fixed line.
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[@jimiwills]

If you take a left-handed helix into the fourth dimension can you turn it round and put it back in to our 3 dimensions so that it's now right handed?

[@discovermaths]

Yes, just as you can lift a (2-D) spiral, rotate it in 3-D, and put it back as a spiral of opposite handedness.

[@jimiwills]

Also... Is there a 4D version of a helicoid?

[@discovermaths]

Yes, both the helicoid and catenoid can be generalised in higher dimensions, including the fourth.